# Solve 2x 10 ## Absolute value equations

|2x|=10

### Step  1  :

#### Rearrange this Absolute Value Equation

Absolute value equalitiy entered
|2x| = 10

### Step  2  :

#### Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is |2x|

For the Negative case we'll use -(2x)

For the Positive case we'll use (2x)

### Step  3  :

#### Solve the Negative Case

-(2x) = 10

Multiply
-2x = 10

Divide both sides by 2
-x = 5

Multiply both sides by (-1)
x = -5
Which is the solution for the Negative Case

### Step  4  :

#### Solve the Positive Case

(2x) = 10

Divide both sides by 2
x = 5

Which is the solution for the Positive Case

x=-5
x=5

### Two solutions were found :

1.  x=5
2.  x=-5
Sours: https://www.tiger-algebra.com/drill/%7C2x%7C=10/

We have two responses for you

Hi Helen,

Let me illustrate with a similar problem.

solve the following inequality for x
-6 < 4 - 5x ≤ 9

You can solve an inequality as you would solve an equality (equation) with one change. If you multiply or divide both sides of the inequality by a negative number, the direction of the inequality reverses. In my problem, as in yours, there are two inequalities, -6 < 4 - 5x and 4 - 5x ≤ 9 but if you are careful you can solve both at the same time.

The object is to manipulate the inequalities and end with a statement of the form

first number < x < second number

-6 < 4 - 5x ≤ 9

First I add -4 to both sides of each inequality to get

-6 -4 < 4 - 5x -4 ≤ 9 -4

or

-10 < - 5x ≤ 5

I don't want the negative sign between the inequalities so I multiply through by -1. Since -1 is negative this reverses the direction of the inequalities.

10 > 5x ≥ -5.

Since the number line is arranged so that larger numbers are to the right you might find it more natural to write this

-5 < 5x ≤ 10.

The final step is to divide through by 5 to get

-1 < x ≤ 2.

Penny

Helen, to answer these questions, you simply treat it like an equation
with three sides (whatever you do to one side, you have to do to the
other two as well) except that multiplying or dividing by a negative
causes the direction of the inequalities to change.

Here's an example:

20 > 7-4x > 4

I want x by itself in the middle, so first I subtract 7 from all sides:
20 - 7 > 7 - 4x - 7 > 4 - 7
13 > -4x > -3

Now I divide all sides by -4. I have to flip the direction of the
inequality because I am dividing by a negative:
13 / (-4) < -4x / (-4) < -3 / (-4)
-13/4 < x < 3/4

So x is between -13/4 and 3/4. I can write this as (-13/4, 3/4)

Now you try it with -1 < 5-2x < 10.

Cheers,
Stephen La Rocque.

Sours: http://mathcentral.uregina.ca/QQ/database/QQ.09.08/h/helen2.html  ### Most Used Actions

 \mathrm{simplify} \mathrm{solve\:for} \mathrm{expand} \mathrm{factor} \mathrm{rationalize}
Related »Graph »Number Line »Examples » Our online expert tutors can answer this problem

Get step-by-step solutions from expert tutors as fast as 15-30 minutes. Your first 5 questions are on us!

In partnership with

You are being redirected to Course Hero

Let's Try Again :(

Try to further simplify ### Examples

equation-calculator

2x=10-3

en

Sours: https://www.symbolab.com/solver/equation-calculator/2x=10-3
Factor over the complex numbers: x^2+2x+10

## Linear equations with one unknown

### Step  1  :

#### Pulling out like terms :

1.1     Pull out like factors :

2x - 10  =   2 • (x - 5)

### Step  2  :

#### Equations which are never true :

2.1      Solve :    2   =  0

This equation has no solution.
A a non-zero constant never equals zero.

#### Solving a Single Variable Equation :

2.2      Solve  :    x-5 = 0

Add  5  to both sides of the equation :
x = 5

### One solution was found :

x = 5
Sours: https://www.tiger-algebra.com/drill/2x-10=0/

## 10 solve 2x

.

x^3 - 5x^2 + 2x - 10 = 0. For what real value of x is the equation above true?

.

### Similar news:

.

535 536 537 538 539